NDLI: Point process-based Monte Carlo estimation

Content Provider	Springer Nature Link
Author	Walter, Clément
Copyright Year	2015
Abstract	This paper addresses the issue of estimating the expectation of a real-valued random variable of the form $$X = g(\mathbf {U})$$ where g is a deterministic function and $$\mathbf {U}$$ can be a random finite- or infinite-dimensional vector. Using recent results on rare event simulation, we propose a unified framework for dealing with both probability and mean estimation for such random variables, i.e. linking algorithms such as Tootsie Pop Algorithm or Last Particle Algorithm with nested sampling. Especially, it extends nested sampling as follows: first the random variable X does not need to be bounded any more: it gives the principle of an ideal estimator with an infinite number of terms that is unbiased and always better than a classical Monte Carlo estimator—in particular it has a finite variance as soon as there exists $$k \in \mathbb {R}> 1$$ such that $${\text {E}}\left[ X^k \right] < \infty $$ . Moreover we address the issue of nested sampling termination and show that a random truncation of the sum can preserve unbiasedness while increasing the variance only by a factor up to 2 compared to the ideal case. We also build an unbiased estimator with fixed computational budget which supports a Central Limit Theorem and discuss parallel implementation of nested sampling, which can dramatically reduce its running time. Finally we extensively study the case where X is heavy-tailed.
Starting Page	219
Ending Page	236
Page Count	18
File Format	PDF
ISSN	09603174
Journal	Statistics and Computing
Volume Number	27
Issue Number	1
e-ISSN	15731375
Language	English
Publisher	Springer US
Publisher Date	2015-11-26
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Nested sampling Central limit theorem Heavy tails Rare event simulation Last particle algorithm Statistics and Computing/Statistics Programs Artificial Intelligence (incl. Robotics) Statistical Theory and Methods Probability and Statistics in Computer Science
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics Statistics, Probability and Uncertainty

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